Analysis of dynamical processes under consideration of polymorphic uncertainty

• The numerical analysis of structures requires a realistic nonlinear simulation model and the consideration of uncertainty.
• Polymorphic uncertainty models can consider more than one uncertainty characteristic within an uncertain variable.
• The uncertainty model fuzzy probability based fuzzy randomness (fp-fr) allows a separated evaluation of these characteristics.
• By application of fp-fr variability, impression and incompleteness can be taken simultaneously into account.
• Two methods and algorithms for time-dependent structural analysis under consideration of uncertainty are formulated.

The numerical analysis of structures requires, on the one hand, a realistic nonlinear structural model and related computational algorithms and on the other hand, the consideration of data uncertainty. The uncertainty results from variations in structural parameters, incomplete knowledge about previous excitations, the quality of the numerical model itself and/or missing information (data) about parameters in the model. The consideration of more than one uncertainty characteristic within uncertain parameters is possible by the application of polymorphic uncertainty models. These models allow taking variability, impression and incompleteness simultaneously into account and enable a separated evaluation of the influence of each uncertainty characteristic on the results. With the aid of these models, structural engineers can assess the improvement capacity and take further steps to reduce the uncertainty, e.g. for incompleteness. In this contribution, two methods for time-dependent structural analysis under consideration of uncertainty are formulated. The methods differ from each other with respect to uncertainty analysis and time step integration and can be used for existing deterministic numerical/analytical solutions. The proposed examples demonstrate the applicability of both methods.